Answer
$147\sqrt3$
Work Step by Step
The radius is the short side of a 30-60-90 triangle containing half of the base of the triangle and the apothem. Thus, we obtain:
$ l = 7\sqrt{3}$
Since this is half of a side, we see that a whole side is $ s = 14\sqrt{3}$
We use the equation for the area of a equilateral triangle:
$A = \frac{\sqrt3}{4}s^2 = \frac{\sqrt3}{4}(14\sqrt3)^2 = 147\sqrt3$
